sin A/2 = +-[(1 – cos A) / 2] cos A/2 = +-[(1 + cos A) / 2] tan A/2 = +-[(1 – cos A) / (1 + cos A)] (or) sin A / (1 + cos A) (or) (1 – cos A) / sin A. They also include the sum and products of identities. Double Angle Identities. Each of the formulas below can be easily obtained by with the help of the ratio of the faces of the right-angled triangular. = 2sin(x) cos(x) = [2tan x/(1+tan 2 x)] = cos 2 (x)-sin 2 (x) = [(1-tan 2 x)/(1+tan 2 x)] cos(2x) = 2cos 2 (x)-1 = 1-2sin 2 (x) tan(2x) = [2tan(x)]/ [1-tan 2 (x)] cot(2x) = [cot 2 (x) – 1]/[2cot(x)] sec (2x) = sec 2 x/(2-sec 2 x) cosec (2x) = (sec x.1 cosec x)/2. The more complex formulas can be calculated using trigonometric functions formulas. Triple Angle Identities. Reciprocal identities are often used to make trigonometric issues easier. = 3sin x – 4sin 3 x = 4cos 3 x – 3cos x = [3tanx-tan 3 x]/[1-3tan 2 x] Reciprocal Identifications.

Identity of products.1 cosec th = 1 sin th secth is 1/cos th the cot = 1/tan sin = 1/cosec cos th = 1 sec th the tan = 1/cot. 2sinxcosy=sin(x+y)+sin(x-y) 2cosxcosy=cos(x+y)+cos(x-y) 2sinxsiny=cos(x-y)-cos(x+y) Pythagorean Identities. Sum of the Identities. Sin 2th + Cos 2th = 1+ Tan 2 the = Sec 2th 1 + Cot 2 the result is Cosec 2 Th.1 sinx+siny=2sin((x+y)/2) . cos((x-y)/2) sinx-siny=2cos((x+y)/2) . sin((x-y)/2) cosx+cosy=2cos((x+y)/2) . cos((x-y)/2) cosx-cosy=-2sin((x+y)/2 . sin((x-y)/2) Sum and Different Identity. inverse Trigonometric Functions. = sin(x)cos(y) + cos(x)sin(y) = cos(x)cos(y) – sin(x)sin(y) = (tan x + tan y)/ (1-tan x tan y) = sin(x)cos(y) – cos(x)sin(y) = cos(x)cos(y) + sin(x)sin(y) = (tan x-tan y)/ (1+tan x tan y) Inverse trigonometric function is the inverse ratio of trigonometric ratios.1 Half-Angle Identities. This is the trigonometric basic function, Sin Th = x could be modified to Sin 1.x = th. sin A/2 = +-[(1 – cos A) / 2] cos A/2 = +-[(1 + cos A) / 2] tan A/2 = +-[(1 – cos A) / (1 + cos A)] (or) sin A / (1 + cos A) (or) (1 – cos A) / sin A. The x value can be expressed in decimals, whole numbers and fractions as well as exponents.1 Double Angle Identities.

For th = 30deg , we can have th = Sin -1 (1/2). = 2sin(x) cos(x) = [2tan x/(1+tan 2 x)] = cos 2 (x)-sin 2 (x) = [(1-tan 2 x)/(1+tan 2 x)] cos(2x) = 2cos 2 (x)-1 = 1-2sin 2 (x) tan(2x) = [2tan(x)]/ [1-tan 2 (x)] cot(2x) = [cot 2 (x) – 1]/[2cot(x)] sec (2x) = sec 2 x/(2-sec 2 x) cosec (2x) = (sec x.1 cosec x)/2. Each of the trigonometric equations can be converted into formulas for inverse trigonometric functions. Triple Angle Identities. Arbitrary Values The inverse trigonometric proportion formula that can be used for any value is applicable to all Six trigonometric formulas. = 3sin x – 4sin 3 x = 4cos 3 x – 3cos x = [3tanx-tan 3 x]/[1-3tan 2 x] For the trigonometric functions that are inverse that include sine, tangent and cosecant and cosecant, the negative values is translated into those of the functions that are negative.1 Identity of products.

In the case of functions such as cosecant, secant, and cotangent and cotangent, and cotangent, the domain’s negatives will be translated to an addition of function from the value of p. 2sinxcosy=sin(x+y)+sin(x-y) 2cosxcosy=cos(x+y)+cos(x-y) 2sinxsiny=cos(x-y)-cos(x+y) Sin -1 (-x) = -Sin -1 x Tan -1 (-x) = -Tan -1 x Cosec -1 (-x) = -Cosec -1 x Cos -1 (-x) = p – Cos -1 x Sec -1 (-x) = p – Sec -1 x Cot -1 (-x) = p – Cot -1 x.1 Sum of the Identities. The inverse trigonometric function of complementary and reciprocal functions are comparable to the trigonometric fundamental functions. sinx+siny=2sin((x+y)/2) . cos((x-y)/2) sinx-siny=2cos((x+y)/2) . sin((x-y)/2) cosx+cosy=2cos((x+y)/2) . cos((x-y)/2) cosx-cosy=-2sin((x+y)/2 .1 sin((x-y)/2) The reciprocal relationships of the fundamental trigonometric functions sine-cosecant and cos-secant, and tangent-cotangent, could be translated into the inverse trigonometric function. inverse Trigonometric Functions. The complementary functions like since-cosine and tangent-cotangent and secant cosecant can be translated as: Inverse trigonometric function is the inverse ratio of trigonometric ratios.1 Reciprocal Functions: Inverse trigonometric formulas of inverted sine and inverse cosine, and inverse tangent could be expressed using the following formulas. This is the trigonometric basic function, Sin Th = x could be modified to Sin 1.x = th.

Sin -1 x = Cosec -1 1/x Cos -1 x = Sec -1 1/x Tan -1 x = Cot -1 1/x.1 The x value can be expressed in decimals, whole numbers and fractions as well as exponents. Complementary Functions: the complimentary roles of sine-cosine and tangent-cotangent secant-cosecant and sine-cosine, add up to p/2.

For th = 30deg , we can have th = Sin -1 (1/2). Sin -1 x + Cos -1 x = p/2 Tan -1 x + Cot -1 x = p/2 Sec -1 x + Cosec -1 x = p/2.1 Each of the trigonometric equations can be converted into formulas for inverse trigonometric functions. Trigonometric Functions and Derivatives. Arbitrary Values The inverse trigonometric proportion formula that can be used for any value is applicable to all Six trigonometric formulas.

The trigonometric function’s differentiation yields the slope of tangent of the Sinx curve.1 For the trigonometric functions that are inverse that include sine, tangent and cosecant and cosecant, the negative values is translated into those of the functions that are negative. The method of differentiation from Sinx will be Cosx and, by applying the x value to the degrees of Cosx we can calculate what is the slope of the slope of Sinx at a specific place.1 In the case of functions such as cosecant, secant, and cotangent and cotangent, and cotangent, the domain’s negatives will be translated to an addition of function from the value of p. The formulas for trigonometric functions that are differentiated are helpful to figure out the equation for a tangentand normal to detect errors in calculations.1 Sin -1 (-x) = -Sin -1 x Tan -1 (-x) = -Tan -1 x Cosec -1 (-x) = -Cosec -1 x Cos -1 (-x) = p – Cos -1 x Sec -1 (-x) = p – Sec -1 x Cot -1 (-x) = p – Cot -1 x. d/dx. The inverse trigonometric function of complementary and reciprocal functions are comparable to the trigonometric fundamental functions. Sinx = Cosx D/DX.1

The reciprocal relationships of the fundamental trigonometric functions sine-cosecant and cos-secant, and tangent-cotangent, could be translated into the inverse trigonometric function. Cosx = Sinx d/dx. The complementary functions like since-cosine and tangent-cotangent and secant cosecant can be translated as: Tanx = Sec 2 x d/dx.1 Reciprocal Functions: Inverse trigonometric formulas of inverted sine and inverse cosine, and inverse tangent could be expressed using the following formulas. Cotx = -Cosec 2 x d/dx.Secx = Secx.Tanx d/dx.

Sin -1 x = Cosec -1 1/x Cos -1 x = Sec -1 1/x Tan -1 x = Cot -1 1/x. Cosecx = + Cosecx.Cotx. Complementary Functions: the complimentary roles of sine-cosine and tangent-cotangent secant-cosecant and sine-cosine, add up to p/2.1 Integration of Trigonometric Function.

Sin -1 x + Cos -1 x = p/2 Tan -1 x + Cot -1 x = p/2 Sec -1 x + Cosec -1 x = p/2. A trigonometric integration function is beneficial in determining the area beneath that graph for the trigonometric formula. Trigonometric Functions and Derivatives.

In general, the area beneath that graph in the trigonometric formula can be calculated using any of the axis lines within a certain limit.1 The trigonometric function’s differentiation yields the slope of tangent of the Sinx curve. The combination of trigonometric function is beneficial to find the areas of irregularly shaped plane surfaces.

The method of differentiation from Sinx will be Cosx and, by applying the x value to the degrees of Cosx we can calculate what is the slope of the slope of Sinx at a specific place.1 cosx dx = sinx + C sinx dx = -cosx + C sec 2 x dx = tanx + C cosec 2 x dx = -cotx + C secx.tanx dx = secx + C cosecx.cotx dx = -cosecx + C tanx dx = log|secx| + C cotx.dx = log|sinx| + C secx dx = log|secx + tanx| + C cosecx.dx = log|cosecx – cotx| + C. The formulas for trigonometric functions that are differentiated are helpful to figure out the equation for a tangentand normal to detect errors in calculations.1